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T18-07 Seasonally Adjusted Linear Trend Forecast

Purpose Allows the analyst to create and analyze a "Seasonally Adjusted Linear Trend" forecast. The MAD and MSE for the forecast are calculated, and a various graphical displays are shown: seasonal relationship, historical demand and forecast, as well as several averaging and de-seasonalized representations.

Inputs Historical Time SeriesSeasonality Labels

Outputs Adjusted Seasonal RelativesGraph showing Historical Time SeriesGraph showing Adjusted Seasonal RelativesGraph showing Historical Time Series and Seasonally

Adjusted Linear Trend ForecastVarious graphs showing steps in the forecast method

Limitations 60 Time Series Observations12 Seasonality Labels

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Time Series Techniques

Seasonal Relatives – develops factors based on seasonality. These factors are used to adjust future forecasts Horizon: Intermediate rangeMethod:

Strength: Ability to determine a seasonality factors to adjust future forecasts.

Weakness: Lot of effort when no seasonality exists. Good idea to look at data to determine if seasonality should be

considered.

Complicated Formula involving moving averages, and

centered moving averages. Depends on whether an even

or an odd number of periods are in the seasonality.

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tat timeForecast F

tat time demand historical Actual A where

F A Error Forecast

t

t

tt

Given that a forecast is rarely correct, the methodology you choose should be the one which provides the least error from the actual historical demand. Forecast error is defined as the difference between actual historical demand and the forecast.

Forecast Accuracy

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0 1 2 3 4 5 6 7 8 9 10 11 12

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Forecast Error

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There are two measures used to monitor the accuracy of a forecast. The Mean Absolute Deviation (MAD) and the Mean Squared Error (MSE).

The MAD is the average of the absolute value of the forecast errors. The MSE is the average of the squared forecast errors.

Note: The formula for the MSE shown above may vary slightly. Some textbooks divide the sum of the squared errors by n-1 rather than n.

2)( average MSE

)abs( average MAD

Monitoring the Forecast

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A company has looked at its quarterly sales over the last three years, and believes that in addition to a linear trend a seasonal pattern is present.

Determine the adjusted seasonal relatives and create a seasonally adjusted linear trend forecast.

Seasonally Adjusted Linear Trend Forecast Example

Label TimeTime

SeriesQ1 1 14.00Q2 2 18.00Q3 3 35.00Q4 4 46.00Q1 5 28.00Q2 6 36.00Q3 7 60.00Q4 8 71.00Q1 9 45.00Q2 10 54.00Q3 11 84.00Q4 12 88.00

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Input the Seasonality Label and Time Series in the light green cells.

The adjusted seasonal relatives and seasonal forecast are automatically calculated.

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A graph showing the Time Series (Historical Demand) is automatically produced.

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A graph showing the Time Series (Historical Demand), Moving Average, and Centered Moving Average is automatically produced.

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A graph showing the Adjusted Seasonal Relatives is automatically produced.

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A graph showing the Time Series (Historical Demand) and Deseasonalized Demand is automatically produced.

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A graph showing the Time Series (Historical Demand), Deseasonalized Demand, and Deseasonlized Forecast is automatically produced.

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A graph showing the Time Series (Historical Demand), Seasonally Adjusted Linear Trend Forecast is automatically produced.